Final answer:
The lines y=2/1x+8 and y=1/2x-1 are in a directly proportional relationship, as an increase in x leads to a corresponding increase in y.
Step-by-step explanation:
The lines y=2/1x+8 and y=1/2x-1 are in a directly proportional relationship. Two values or constants are directly proportional when a change in one leads to the same change in the other. In this case, the slope of both lines is positive, indicating that as x increases, y also increases.
We can see this relationship by comparing the two equations. The first equation, y=2/1x+8, has a slope of 2/1, which means that for every one unit increase in x, y increases by 2 units. The second equation, y=1/2x-1, has a slope of 1/2, indicating that for every two unit increase in x, y increases by 1 unit.
Therefore, both lines have a directly proportional relationship, as an increase in x leads to a corresponding increase in y.